Determine if the expression \( -b^{2} c^{3}+b^{3} d^{3}-d b \) is a polynomial or not. If it is polynomial, state the type and degree of the polynomial. Answer Attempt 1 out of 2 The given expression \( \sim \) a polynomial.

Yes, the expression \( -b^{2} c^{3} + b^{3} d^{3} - d b \) is a **polynomial**. Let's analyze its type and degree: ### Type of Polynomial: - **Multivariate Polynomial**: This polynomial involves multiple variables (\(b\), \(c\), and \(d\)). A polynomial with more than one variable is termed multivariate. ### Degree of the Polynomial: - The **degree** of a polynomial is the highest sum of the exponents of the variables in any single term. Let's examine each term: 1. **\(-b^{2} c^{3}\)**: - Exponents: \(b^2\) and \(c^3\) - Sum of exponents: \(2 + 3 = 5\) 2. **\(b^{3} d^{3}\)**: - Exponents: \(b^3\) and \(d^3\) - Sum of exponents: \(3 + 3 = 6\) 3. **\(-d b\)**: - Exponents: \(d^1\) and \(b^1\) - Sum of exponents: \(1 + 1 = 2\) - **Highest Sum of Exponents**: The second term \(b^{3} d^{3}\) has the highest sum of exponents, which is **6**. ### Conclusion: - **Type**: Multivariate Polynomial - **Degree**: 6 Therefore, \( -b^{2} c^{3} + b^{3} d^{3} - d b \) is a **multivariate polynomial of degree 6**.